FFT spectrum analyzer数字信号处理第二次大作业.docx

FFT spectrum analyzer数字信号处理第二次大作业.docx

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FFTspectrumanalyzer数字信号处理第二次大作业

FFTspectrumanalyzer

basedonMatlab

NAME

：

XXXXX

StudentID

：

00000000000

Professor

：

何岭松

Date

：

2013-10-08

Abstract

Fouriertransformispowerfulmethodinsignalprocess.Itcantransformthesignalfromtimedomaintofrequencydomain.Infrequencydomainsomecharacteristicismoreobviousthanitintimedomain.Forthediscretesignal,thereisDiscreteFourierTransform（DFT）.ButtheamountofcalculationinDFTislarge,tospeedupincalculation,thereisFastFourierTransform（FFT）.ForDFTandFFT,asthespectrumisdiscrete,andonlythefrequencysamplingpointiscalculated,itcausedthefenceeffect.Andtheenergyleakageforcycleextension.Toreducethefenceeffect,windowfunctionisneeded.

Inthisproject,FFTisusedtoanalyzethespectrumofthesignal.Thesignalcanbegeneratedinthreeways,signalgenerator,readfromwavfilesandinputfromthesoundcard.Toreducethefenceeffect,windowfunctionissupported.

Keywords:

FFTwavfilesoundcardinputwindowfunction

Content

1.Introduction1

2.Method2

2.1Signalspectrumanalysis2

2.1.1ContinuousFourierTransform2

2.1.2DiscreteFourierTransform（DFT）2

2.1.3FastFourierTransform（FFT）3

2.2WindowFunction3

2.3SignalSource4

2.4Zoomspectrum5

3.Results5

3.1Interfaceoftheprogram5

3.2FFTthesignalfromsignalgenerator7

3.3Readthewavfileandspectrumanalysis9

3.4Soundcardinputandspectrumanalysis10

3.5ZoomFFT10

3.6Windowfunction10

4.Conclusions13

5.References13

1.Introduction

Oneofthemostcommonlyusedmethodinsignalprocessingisthespectrumanalysis.Ittransformthesignalfromtimedomaintofrequencydomain.Forsomesignal,thetimedomainanalysisisverydifficult,andsomecharacteristicsishardtoobtainfromtimedomainanalysis,suchasifthesignalhasacycle,thecompositionofthesignal.Thosecharacteristicsisveryclearinfrequencydomain.

ThemethodthattransformthesignalfromtimedomainintofrequencydomainisFourierTransform.Forthecontinuoussignal,integrationiscalculated.Forthediscretesignal,thereistheDiscreteFourierTransform（DFT）.Thesummationisinsteadtheintegration.Asthesummationislargecalculation,especiallywhenthesamplepointislarge.AgoodwaytospeedupthecalculationistheFastFourierTransform（FFT）.FFTismuchfastertheDFT,especiallywhenthesamplepointislarge.Forexample,forasignalof1024points,theFFTisfasterthantheDFT100times.

Generally,thesignaliscontinuous,whenwegetthesignal,wediscretethesignalwithasamplesignal.ForDFTorFFT,wediscretethespectrum,andonlycalculatethefrequencysamplingpoints.Thefrequencythatwedon’tsampledisignored,whichcausedtheFenceEffect.Forthesignalislongintime,it’snotpossibletosamplethewholesignal.Infact,onlyasectionofthesignalissampled,andthenextendthesignalwiththecycleassampled.Thesignalofcycleextensionisdifferentwiththeoriginal.Thiscausedtheenergyleakage.Toreducethefenceeffect,windowfunctionisused.Inthisproject5windowfunctionissupported,theyarerectanglewindow,trianglewindow,hanningwindow,hammingwindowandblackmanwindow.Usercanselectdifferentwindowfunctionbyagroupofradiobutton.

TheresultofDFTorFFTisgivingthewholespectrum.Insomecase,wejustinterestonalittlerangeofthespectrum.Forthiscase,zoomtechniquesofthespectrumisneeded.Inthisproject,it’sincluded.

Inthisproject,thesourcesignalthattobeanalyzeisgeneratedinthreeways,signalgenerator,readfromwavfileandrecordfromsoundcard.

2.Method

2.1Signalspectrumanalysis

Thespectrumanalysisisoneofthemostcommonlymethodinsignalprocessing.Forsomecharacteristicofthesignalistimedomainisnoteasytoget,ittransformthesignaloftimedomainintofrequencydomain,andanalyzethesignalinfrequencydomain.

2.1.1ContinuousFourierTransform

Forthecontinuoussignal,theFouriertransformisshowas

isthesignalintimedomain.

isthesignalinfrequencydomain.Forthesignaliscontinuous,tocalculatetheformofthesignalinfrequencyintegrationisneeded.

2.1.2DiscreteFourierTransform（DFT）

Asdigitalsignalisnotcontinuousbutdiscrete.It’simpossibletocalculateallfrequencypoints.Tocalculatethespectrum

it’sfirsttodiscretethefrequency:

Nisthesizeofsamplepoint,andFsisthesamplefrequency.Then,thefrequencypointis

Finally,thespectrumofthesignalis

k=0,1,2,...,N-1

Where,Nisthesizeofsamplepoint,

2.1.3FastFourierTransform（FFT）

From2.1.2,wefindthatDFTcancalculatetheX（f）,butifweextendit,wegetthis.

Where

Fromthis,wecanfindthatalargecalculationsofsineandcosinearerepeat.Ifwereducetheserepeatcalculation,itwillbemuchfaster.That’swhatFFThasdone.Asit’sname,FFTisfasterthanDFT,thelargerthepointsare,thefastertheFFTiscomparedwithDFT.Forasignalof1024points,theFFTis100timesfasterthenDFT.

2.2WindowFunction

AsDFTandFFT,spectrumisdiscrete,andonlycalculatethefrequencysamplingpoint,andotherpointisnot.SoFenceeffectiscaused,andsomeinformationofthespectrumismissed.

Thesignalintimedomainislong,evensomeareendless.It’simpossibletosampleallthesignal.Infact,thecommonmethodissampleasectionasacycleofthesignal,andthenextendthesignal.Asthesignalofcycleextensionisdifferentwiththeoriginalsignal,Energyleakageiscaused.Fromthemathematicalpointofview,thisprocesscanbedescribedas

x（t）:

Originalsignal.

w（t）:

Cutoffwindowfunction

y（t）:

Extensionsignal.

Theenergyleakageisnotalwaysbadforanalysis.Itreducedthefenceeffect,especiallywhenaappropriatewindowfunctionw（t）ischosen.

Thereare5windowfunctionissupportedinthisproject,theyareRectangleWindow,TriangleWindow,HanningWindow,HammingWindowandBlackmanWindow.Themathematicexpressionofthewindowfunctionsarelistintable1.

Table1themathematicexpressionandtheAmplitudecorrectioncoefficient.

Windowfunction

Mathematicexpression

Amplitudecorrectioncoefficient

Rectanglewindow

1

Hanningwindow

2

Hammingwindow

1.852

Trianglewindow

2

Blackmanwindow

2.381

2.3SignalSource

Inthisprojectthesignalgeneratedinthreeways.ThefirstisfromthesignalgeneratorbasedonMatlab,thesecondisreadfromwavfilesandthethirdisfromcomputer’ssoundcard.

Forthesignalgenerator,theprogramsupport4types,sine,cosine,squareandtrianglewave.Theexpressionofthewaveislistintable2.

Table2theexpressionofthesignal

Signaltype

Mathematicexpression

Sinewave

Cosinewave

Squarewave

Trianglewave

InMatlab,therefunctionstoreadsignalfromwavfileandrecordfromthesoundcard.Thefunctiontoreadwavfileis

[Y,Fs,NBITS]=wavread（FILE）;

Yisthedatareadfromthewavfile,Fsisthesamplerate,andNBITSisthenumberofbitspersampleusedtoencodethedatainthefile.

2.4Zoomspectrum

ForthenormalFFT,itshowsallthefrequency.Sometimes,thecharacteristicsfocusedonlyinasmallrangeinfrequency.FromthespectrumfromthenormalFFT,it’snotconvenienttoobservethesignal.Thus,zoomspectrumisneeded.

Intheproject,atfirstwemakethesignalaZtransform,andthenanalyzethesignal.Sothespectrumisintherangethatweinterestedin.

3.Results

3.1Interfaceoftheprogram

Thefinalinterfaceoftheprogramisshowinfig.3.1

Fig.3.1thefinalinterfaceoftheprogram

Asshowninfig.3.1,theinterfacedivide6parts.Thefirstpartistwoaxes.Theyshowthesignalintimedomainandfrequencydomainrespectively.

Thesecondpartisthewindowfunctionselectionpart.Inthispart,fivewindowfunctionaresupported.TheyareRectanglewindow,Trianglewindow,Hanningwindow,HammingwindowandBlackmanwindow.Thispartisshowninfig.3.2.

Thethirdpartisthesignalgenerator.Itsimilarwithproject1.It’snomoredetaildiscussedhere.It’sshowninfig.3.3

Fig3.2windowfunctionselectionfig.3.3signalgenerator

Theforthpartisthereadwavfilepart.Fromthepushbuttonselectwavfileusercanselectthewavfile.Theretwoedittextboxinthispart,withwhichtheusercansetthesamplesection.Thispartisshowninfig3.4.

Thefifthpartistherecordpart.Withthispart,theusercaninputthesoundfromthecomputer’ssoundcard.Thereare4parametersshouldbeset,theyaresamplepoint,sampleFrequency,channelofthesoundandthenumberofthedatatoencode.It’sshowinfig3.5

Thesixthpartisfrequencyspectrumrefinement.Withthispart,usercanzoomtheinterestedfrequencyrange.Thispartisshowninfig3.6

Fig3.4wavfilereadpartfig3.5soundcardinputpart

Fig3.6Frequencyspectrumrefinementpart

3.2FFTthesignalfromsignalgenerator

Thesignalthatsignalgeneratorgeneratedisthestandardsignal.Theyaresinewave,cosinewave,squarewaveandtrianglewave.Thetimeandfrequencydomainwaveformisshowninfig3.7tofig.3.10.

Fig.3.7thesinewavegenerator（

）

Fig.3.8thecosinewavegenerator（

）

Fig.3.9thesquarewave（

）

Fig.3.10thetrianglewave（

）

3.3Readthewavfileandspectrumanalysis

Fig.3.11Thetelephonedialtonesimulation

Thisfigisreadawavfileandsamplethe1to30720points.

3.4Soundcardinputandspectrumanalysis

Fig3.12thewaveformofthesoundinputfromsoundcard

Fig3.12showsthewaveforminputfromthesoundcard.Thenumberofsamplepointis20480,samplefrequency